Grid-Tie Inverters - Designed to convert solar energy directly into AC without the use of batteries.  Can be used with net-metering to sell electricity back to your electric utility.

Square wave inverters are a type of grid-tie inverter that is cheap but doesn't do a good of a job digitizing the current, reducing the quality of the power.

A synchronous inverter is a grid-tie inverter that uses the signal from the utility to feed power onto the wave using high speed switching.
Microinverters are autonomous inverters that are mounted to the back of each module.  This is a recent development in the solar industry.  They make it easier to design systems and increase efficiency.  Micro inverters should be shaded.
Stand Alone Inverters - Designed to convert energy from batteries which are charged from solar panels.